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Piecewise holomorphic systems and regularization of Filippov systems

Grant number: 22/12123-9
Support Opportunities:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): March 01, 2023
Effective date (End): February 29, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Paulo Ricardo da Silva
Grantee:Gabriel Alexis Rondón Vielma
Supervisor: Armengol Gasull
Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Research place: Universitat Autònoma de Barcelona (UAB), Spain  
Associated to the scholarship:20/06708-9 - Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles, BP.PD


We will study the number of limit cycles of piecewise holomorphic systems, which is related to the famous Hilbert Problem 16 for piecewise vector fields. Also, we will investigate slow-fast systems in C^2, which can be used in the regularization process of discontinuous fields in R^4 with discontinuity surface with codimension 2. Also, we are interested in investigating the typical singularities of slow-fast systems that arise from (linear or non-linear) regularizations. (AU)

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